Simplify
(2^-1∙7^-4)^-2
Is it 1/2^2*7^8 OR simply just 2^2*7^8
2^2 * 7^8
or
4*7^8
So no 1 goes above that? as in
1
-------
2^2*7^8?
no, the negative exponents change to + when you multiply -*-
THANKS!
To simplify the given expression, (2^-1 * 7^-4)^-2, we can follow these steps:
Step 1: Simplify the inside of the parentheses.
- A negative exponent in the numerator can be made positive by moving it to the denominator. So, 2^-1 becomes 1/2.
- Similarly, 7^-4 becomes 1/7^4.
Now, the expression becomes ((1/2)(1/7^4))^-2.
Step 2: Simplify the expression within the parentheses.
- The product of two numbers raised to a power can be simplified by multiplying the numbers and raising them to the same power. So, (1/2)(1/7^4) becomes 1/(2 * 7^4).
Now, the expression becomes (1/(2 * 7^4))^-2.
Step 3: Simplify the expression by applying the exponent.
- When raising a fraction to a negative exponent, the reciprocal of the fraction is taken and the exponent becomes positive. So, (1/(2 * 7^4))^-2 becomes 1^2 / ((2 * 7^4)^2).
- 1 raised to any power is still 1. So, the expression becomes 1 / ((2 * 7^4)^2).
Therefore, the simplified form of (2^-1 * 7^-4)^-2 is 1 / ((2 * 7^4)^2).