MCA Grade 8 The Number System. Practice it free.

The Product of Powers Property says that powers with the same base are multiplied by adding the exponents, written $x^{m} \cdot x^{n} = x^{m+n}\textsf{.}$ The numerator is $2^{7} \cdot 2^{4} = 2^{7+4} = 2^{11}\textsf{.}$ The Quotient of Powers Property then subtracts the exponents of powers with the same base, written $\dfrac{x^{m}}{x^{n}} = x^{m-n}\textsf{.}$ So $\dfrac{2^{11}}{2^{6}} = 2^{11-6} = 2^{5}$ and $n = 5\textsf{.}$

$4 \times 4 \times 4 = 64$, so $\sqrt[3]{64} = 4$.

$\pi \approx 3.14159$.

The Negative Exponent Property says that a nonzero base raised to a negative exponent equals the reciprocal of that base raised to the positive exponent, written $a^{-n} = \dfrac{1}{a^{n}}\textsf{.}$ Applying the property, $a^{-2} = \dfrac{1}{a^{2}}\textsf{.}$

Take the positive square root: $x = \sqrt{169} = 13$ because $13 \times 13 = 169$.

$\sqrt{2} \approx 1.414$.

The Power of a Product Property says that a product raised to a power equals each factor raised to that power, written $(ab)^{n} = a^{n} \cdot b^{n}\textsf{.}$ Here $(3 \cdot 7)^{4} = 3^{4} \cdot 7^{4}$, so $a = 4\textsf{.}$

$12 \times 12 = 144$, so $\sqrt{144} = 12$.