Determine the exponent that makes each equation true.

A. 16^x=1/16
B. 10^x=0.01

pls

1/16 = 1/16^1 = 16^-1

.01 = 1/100 = 1/10^2 = 10^-2

To determine the exponent that makes each equation true, we need to rewrite the equations in exponential form. The general exponential form is "base^exponent = result".

A. 16^x = 1/16
In this equation, the base is 16. We want to find the exponent that makes the equation true, so we need to rewrite 1/16 as a power of 16. 1/16 can be expressed as 16^-2, since a negative exponent means the reciprocal of the base. Therefore, our equation becomes 16^x = 16^-2.

Since the base on both sides of the equation is the same, we can equate the exponents. Therefore, x = -2 is the exponent that makes the equation true.

B. 10^x = 0.01
In this equation, the base is 10. We want to find the exponent that makes the equation true, so we need to rewrite 0.01 as a power of 10. 0.01 is equivalent to 10^-2.

Therefore, our equation becomes 10^x = 10^-2.
Again, since the base on both sides of the equation is the same, we equate the exponents. Therefore, x = -2 is the exponent that makes the equation true.

In both cases, the exponent that makes the equation true is -2.