To simplify the given expression, we can use the rule of exponents that states: 𝑎^(𝑚) / 𝑎^(𝑛) = 𝑎^(𝑚−𝑛).
Using this rule, we can rewrite the expression as:
5^(-3 + 7) / 5^(-7) = 5^4 / 5^(-7)
Using another rule of exponents, 𝑎^𝑚 / 𝑎^n = 𝑎^(𝑚−𝑛), we can subtract the exponents:
5^4 / 5^(-7) = 5^(4-(-7)) = 5^(4+7) = 5^11
Therefore, the expression is equivalent to 5^11.
The correct answer is D) 5^11.
which expression is equivalent to 5^-3 x 5^7/5^-7
A 5^-42
B 25^-42
C 25^11
D 5^11
3 answers
its b
Apologies for the mistake in the previous response.
To simplify the given expression, we can use the rule of exponents that states: 𝑎^𝑚 × 𝑎^𝑛 = 𝑎^(𝑚+𝑛).
Using this rule, we can rewrite the expression as:
5^-3 × 5^7 / 5^-7 = 5^(7 - 3) / 5^-7 = 5^4 / 5^-7
Using another rule of exponents, 𝑎^𝑚 / 𝑎^n = 𝑎^(𝑚−𝑛), we can subtract the exponents:
5^4 / 5^-7 = 5^(4 - (-7)) = 5^(4 + 7) = 5^11
Therefore, the expression is equivalent to 5^11.
The correct answer is D) 5^11.
To simplify the given expression, we can use the rule of exponents that states: 𝑎^𝑚 × 𝑎^𝑛 = 𝑎^(𝑚+𝑛).
Using this rule, we can rewrite the expression as:
5^-3 × 5^7 / 5^-7 = 5^(7 - 3) / 5^-7 = 5^4 / 5^-7
Using another rule of exponents, 𝑎^𝑚 / 𝑎^n = 𝑎^(𝑚−𝑛), we can subtract the exponents:
5^4 / 5^-7 = 5^(4 - (-7)) = 5^(4 + 7) = 5^11
Therefore, the expression is equivalent to 5^11.
The correct answer is D) 5^11.