What is the value of $(5^{2})^{2} + (2^{2})^{3}$ ?

689

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658

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589

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698

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Solution

The correct option is A 689
By the Laws of Exponents, $(a^{m})^{n} = a^{m n}$ .

So, $(5^{2})^{2} = 5^{4} = 5 \times 5 \times 5 \times 5 = 625$
$(2^{2})^{3} = 2^{6} = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64$

$\Rightarrow (5^{2})^{2} + (2^{2})^{3} = 625 + 64 = 689$

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Similar questions

Q. Find the value of using the column method:
(52)²

Q. Find the value of x, if:
(i) 4x = (52)² − (48)²
(ii) 14x = (47)² − (33)²
(iii) 5x = (50)² − (40)²

Simplify
(i) $2^{\frac{2}{3}} \times 2^{\frac{1}{3}}$
(ii) $2^{\frac{2}{3}} \times 2^{\frac{1}{5}}$
(iii) $7^{\frac{5}{6}} \times 7^{\frac{2}{3}}$
(iv) $(1296)^{\frac{1}{4}} \times (1296)^{\frac{1}{2}}$

Q. The value of (52)

^{2}

is:

Q. Find the value of (52)$^2$.

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What is the value of (52)2+(22)3 ?

The correct option is A 689By the Laws of Exponents, (am)n=amn. So, (52)2=54=5×5×5×5=625 (22)3=26=2×2×2×2×2×2=64 ⇒(52)2+(22)3=625+64=689

What is the value of $(5^{2})^{2} + (2^{2})^{3}$ ?

The correct option is A 689
By the Laws of Exponents, $(a^{m})^{n} = a^{m n}$ .

So, $(5^{2})^{2} = 5^{4} = 5 \times 5 \times 5 \times 5 = 625$
$(2^{2})^{3} = 2^{6} = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64$

$\Rightarrow (5^{2})^{2} + (2^{2})^{3} = 625 + 64 = 689$