what is (5^8 times 5^4)/(5^3)^2

Answer 1

To solve this expression, you simplify each part of the expression using the rules of exponents.

(5^8 * 5^4) / (5^3)^2

Start by simplifying the numerator, 5^8 * 5^4, by adding the exponents since the base (5) is the same.

5^(8 + 4) = 5^12

Now, simplify the denominator, (5^3)^2, by multiplying the exponent inside the parentheses by 2.

5^(3 * 2) = 5^6

The expression now becomes:

5^12 / 5^6

To divide the two exponents with the same base, subtract the exponent of the denominator from the exponent of the numerator.

5^(12 - 6) = 5^6

Therefore, (5^8 * 5^4) / (5^3)^2 simplifies to 5^6.

Answer 2

what is (2^9 times (2^-2)^-3)/(2)

Answer 3

To simplify this expression, let's break it down step by step.

First, let's simplify the exponent (2^-2)^-3. According to the rules of exponents, when you raise a power to another exponent, you multiply the exponents.

(2^-2)^-3 = 2^(-2 * -3) = 2^6.

Next, let's simplify the expression inside the parentheses:

2^9 * 2^6 = 2^(9 + 6) = 2^15.

Finally, we divide the resulting expression by 2:

2^15 / 2 = 2^(15 - 1) = 2^14.

Therefore, the simplified form of (2^9 * (2^-2)^-3) / 2 is 2^14.