Mathematics

Mathematics

Problem

Calculate 823×16−148^{\frac{2}{3}}\times16^{-\frac{1}{4}}. a) 88 b) 11 c) 22 d) 44
Intuitive explanation

Fractional exponents are just another way to write roots and powers together—the denominator tells you which root, and the numerator tells you the power. The key is to rewrite both 8 and 16 as powers of the same base (2), then use exponent rules to simplify. Once everything is in terms of a single base, adding and subtracting exponents becomes straightforward.

Intuitive explanation

Fractional exponents are just another way to write roots and powers together—the denominator tells you which root, and the numerator tells you the power. The key is to rewrite both 8 and 16 as powers of the same base (2), then use exponent rules to simplify. Once everything is in terms of a single base, adding and subtracting exponents becomes straightforward.

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