Laws Of Exponents

• The laws of exponents state that anything raised to the first power is itself and anything raised to the zeroth power is just one.
• Exponents can also be applied to integers with negative values, for example, x to the power of negative one, negative two, or negative three.
• The next law on the list, x to the negative nth power equals 1 divided by x to the nth power, explains how to interpret a negative exponent.
• A negative number is the inverse of its positive counterpart, and division is the inverse operation of multiplication, hence a negative exponent is equivalent to repeated division.
• The pattern of a negative exponent can be expressed as a repeated division problem, starting with a 1 and proceeding with the same number of x's multiplied together.
• Mathematicians prefer to express negative exponents in fraction form, where one is divided by the same number of x's multiplied together.
• If we do operations from left to right using a calculator, 0.125 is the answer.
• If the bases of two expressions are the same, they can be combined simply by adding or subtracting the exponents, as per the first and second laws of exponents.
• The law of exponents states that x to the power of m grouped inside parentheses and then that whole group is being raised to the nth power is the same as x to the power of m n.
• 2 to the negative 3rd power is the same as one divided by two to the third power, which simplifies to one over two times two times two, which simplifies to one over eight, which simplifies to 0.125.
• Dividing two expressions with the same base and different exponents can be done by dividing the exponents together, as per the fourth law of exponents.
• Simplifying an expression like x squared cubed can be done by multiplying the exponents together, which equals x to the power of m n, where m times n equals x squared raised to the third power.
• Raising x squared to the negative third power is the same as x to the power of two times negative three, which is x to the negative sixth, and can be rewritten as one over x squared to the positive third power, which simplifies to one over x squared times x squared times x squared, which simplifies to one over six x's being multiplied together.
• Multiplying two expressions with the same base and different exponents can be done by multiplying the exponents together, as per the third law of exponents.
• According to the law, the expression can be simplified by subtracting the bottom exponent from the top, resulting in x to the negative two.
• The third law in this set involves multiplying and dividing expressions with different bases, where the bases are different but the exponents are the same.
• The second law in this set tells us how to divide expressions with the same base.
• If we had 10 x's being multiplied together, we could form different groups and combine them using exponents.
• The first law in this set, which involves multiplication, states that you can rewrite x times y that's being raised to the power of m as x to the m times y to the m.
• The simplified version of the expression is 5 to the power of 3 minus 2, which is also 5 to the first power.
• If you have the expression x squared divided by y squared, you could rewritten as x to the n divided by y to the n.
• These laws work in reverse too, and you can undistribute the exponents if they're the same.
• If you're given the expression x squared times y squared, you could rewrite that as the quantity x times y squared.
• In the expression 5 to the third power divided by 5 to the second power, we can simplify by subtracting the exponents.
• The second law in this set can also be used to divide expressions with different bases, such as x to the fourth power over x to the sixth power.
• The second law in this set, which involves division, states that you can rewrite x divided by y that's being raised to the power of n as x to the n divided by y to the n.
• The laws of exponents state that anything raised to the first power is itself and anything raised to the zeroth power is just one.
• Exponents higher than integer values like x to the second x to the third are also covered by the laws of exponents.
• The laws of exponents also cover expressions involving negative numbers, such as x to the power of negative one or negative two or negative three.
• The law that says x to the negative nth power equals 1 divided by x to the nth power explains how to interpret a negative exponent.
• A negative number is the inverse of its positive counterpart, and division is the inverse operation of multiplication, so a negative exponent is basically repeated division.
• The pattern of a negative exponent can be expressed as a repeated division problem, starting with a 1 and then dividing by the same number of x's multiplied together.
• Mathematicians prefer to express negative exponents in fraction form, where one is divided by the same number of x's multiplied together.
• If you're given the expression x squared times y squared, you could rewrite that as the quantity x times y squared.
• If we had 10 x's being multiplied together, we could form different groups and combine them using exponents.
• If you have the expression x squared divided by y squared, you could rewritten it as x squared divided by y squared.
• In the expression 5 to the third power divided by 5 to the second power, the simplified version is 5 to the first power.
• These laws work in reverse too, and you can undistribute the exponents if they're the same.
• The third law in this set involves multiplying and dividing expressions with different bases, where the bases are different but the exponents are the same.
• The second law in this set tells us how to divide expressions with the same base.