Question

Rewrite the expression (5⁻⁴)³ using only positive exponents

Answer 1

To rewrite (5⁻⁴)³ with positive exponents, multiply the exponents to get 5⁻¹⁲ and then express it as a reciprocal to obtain the final expression 1/(5¹⁲).

Step-by-step explanation:

To rewrite the expression (5⁻⁴)³ using only positive exponents, we must understand the laws of exponents. According to these laws, when we raise a power to a power, we multiply the exponents. The expression given can be seen as a base of 5 with a negative exponent of -4 being raised to the third power.

Implementing the law of exponents here, we would multiply the exponents -4 and 3 together. This can be written step by step as follows:

• (5⁻⁴)³ = 5⁻⁴ × 3
• 5⁻⁴ × 3 = 5⁻¹⁲

Since our goal is to express this with a positive exponent, we recall another law of exponents that a negative exponent represents the reciprocal of the base raised to the positive of that exponent. So now we can convert 5⁻¹⁲:

• 5⁻¹⁲ = 1/(5¹⁲)

Therefore, the expression (5⁻⁴)³ rewritten with positive exponents is 1/(5¹⁲).