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Select all the expressions that are equivalent to 55×555^5 \times 5^5.\newlineMulti-select Choices:\newline(A) 5105^{10}\newline(B) 1510\frac{1}{5^{10}}\newline(C) 15−10\frac{1}{5^{-10}}\newline(D) 1525\frac{1}{5^{25}}

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Simplify exponential expressions using exponent rulesright chevron icon

Full solution

Q. Select all the expressions that are equivalent to 55×555^5 \times 5^5.\newlineMulti-select Choices:\newline(A) 5105^{10}\newline(B) 1510\frac{1}{5^{10}}\newline(C) 15−10\frac{1}{5^{-10}}\newline(D) 1525\frac{1}{5^{25}}
  1. Add Exponents: To solve 55×555^5 \times 5^5, we need to add the exponents since the bases are the same.\newlineCalculation: 55×55=55+5=5105^5 \times 5^5 = 5^{5+5} = 5^{10}
  2. Calculate Result: Now, let's compare the result with each option:\newline(A) 5105^{10} matches our result.\newline(B) 1510\frac{1}{5^{10}} is the reciprocal of 5105^{10}, not equivalent.\newline(C) 15−10\frac{1}{5^{-10}} is also a reciprocal and represents a large positive power of 55, not equivalent.\newline(D) 1525\frac{1}{5^{25}} is the reciprocal of a much larger power of 55, not equivalent.

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