Select all the expressions that are equivalent to 5^-4 * 6^-4. Multi-select Choices: (A)1/30^4 (B)1/30^-4 (C)30^-4 (D)30^-8

Question

Select all the expressions that are equivalent to 5^-4 * 6^-4.   Multi-select Choices: (A)1/30^4 (B)1/30^-4 (C)30^-4 (D)30^-8

Bytelearn · Accepted Answer

Understand Expression: Understand the given expression 5^-4 * 6^-4. We need to find which of the given choices are equivalent to this expression. To do this, we will simplify the expression using the properties of exponents.Simplify Expression: Simplify the expression 5^-4 * 6^-4. Since both 5 and 6 are raised to the same negative exponent, we can combine them under a single exponent. 5^-4 * 6^-4 = (5*6)^-4 = 30^-4Compare to Choices: Compare the simplified expression to the choices. We have simplified the expression to 30^-4. Now we need to check which of the given choices match this expression.  (A) 1/30^4 is the same as 30^-4 because a negative exponent indicates the reciprocal of the base raised to the positive exponent. (B) 1/30^-4 is not equivalent because it suggests the reciprocal of 30 raised to the negative fourth power, which would be 30^4. (C) 30^-4 is exactly what we have found in our simplification. (D) 30^-8 is not equivalent because the exponent is -8, not -4.  So, the expressions equivalent to 5^-4 * 6^-4 are (A) and (C).

Select all the expressions that are equivalent to $5^{-4} \times 6^{-4}$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{30^4}$ $\newline$ (B) $\frac{1}{30^{-4}}$ $\newline$ (C) $30^{-4}$ $\newline$ (D) $30^{-8}$

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Select all the expressions that are equivalent to 5−4×6−45^{-4} \times 6^{-4}5−4×6−4.\newlineMulti-select Choices:\newline(A) 1304\frac{1}{30^4}3041​\newline(B) 130−4\frac{1}{30^{-4}}30−41​\newline(C) 30−430^{-4}30−4\newline(D) 30−830^{-8}30−8

Select all the expressions that are equivalent to $5^{-4} \times 6^{-4}$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{30^4}$ $\newline$ (B) $\frac{1}{30^{-4}}$ $\newline$ (C) $30^{-4}$ $\newline$ (D) $30^{-8}$