Use the properties of exponents to determine whether the equation 10 - 1/3 = exponent 3 root 10 is true or false. Select the response that correctly answers the question and

Question

provides the appropriate justification. (1 point)
• True, because the negative sign moves to the front when writing an equivalent expression.
• False, because according to the Negative Exponent Rule, the equation should be 10-$ = -1
• False, because the Negative Exponent Rule requires that the number be rewritten as a quotient, not as a negative value.
• True, because the Negative Exponent Rule requires that the number be rewritten as a negative value.

Answer 1

The correct response is:

• False, because according to the Negative Exponent Rule, the equation should be 10^{-1/3} = exponent 3 root 10.

Justification: The expression \( 10^{-1/3} \) means \( \frac{1}{10^{1/3}} \), which is not equal to the cube root of 10. The statement compares \( 10^{-1/3} \) with \( \sqrt[3]{10} \), and these two expressions are not equal. Therefore, the equation is false.