Question

Pablo simplified the expression(2^-4)^-2 as shown.

(2^-4)^-2=2^-4*^-2=2^-8


Which statement explains Pablo’s error?

A. He should have added the exponents instead of multiplying them.
B. He should have divided the exponents instead of multiplying them.
C. He should have found 8 as the exponent, not –8.
D. He should have written mc014-3.jpg as mc014-4.jpg.

Answer 1

(2^-4)^-2 = 2^[(-4)*(-2)] = 2^8
answer

C. He should have found 8 as the exponent, not –8.

Answer 2

C. He should have found 8 as the exponent, not –8.

Explanation:

We have been given an expression
`(2^(-4))^(-2)`. We are asked to find the Pablo's error in simplifying the expression.

Let us check steps done by Pablo.

In first step Pablo has simplified
`(2^(-4))^(-2)` to
`(2)^((-2*-4))` using power rule property of exponents which states that to raise a power to a power we have to multiply the exponents. Therefore, his first step is correct.

Now let us check Pablo's second step. We can see that Pablo multiplied -2 by -4 and simplified to
`2^(-8)`.

Since we know that multiplying a negative number with another negative number gives a positive result, therefore, Pablo made mistake in second step. He should have found 8 instead of -8 as the exponent.

The correct steps for simplifying the given expression will be
`(2^(-4))^(-2)=2^((-2*-4))=2^(8)`.

Upon looking at our given option we can see that option C is the correct statement about Pablo's error.