Question

Represent the following expressions as a power of a where a ≠ 0. (a²·a³ ·(a²))⁻¹

Answer 1

To represent (a² · a³ · (a²))⁻¹ as a power of a, we add exponents when multiplying with the same base and apply a negative exponent when raising to a negative power, resulting in a⁻⁷.

Step-by-step explanation:

To represent the expression (a² · a³ · (a²))⁻¹ as a power of a where a ≠ 0, we use the rules for dealing with exponents when we multiply exponentiated quantities together and when we raise them to a power, including the situation when the power is negative.

First, when multiplying expressions with the same base, you add the exponents:

a² · a³ = a²+3 = a⁵.

Now, include the last term (a²). Since the exponential rule applies to everything inside the parentheses, we simply have:

a⁵ · a² = a⁵+2 = a⁷.

Now, because we are dealing with a negative exponent when it's raised to the negative first power ((a⁷)⁻¹), we invert the whole expression, which means:

a⁷¹ = a⁻⁷.

So the final answer is:

a⁻⁷.