Simplify: $3^4 \times 3^6$
Simplify: $\frac{7^{10}}{7^4}$
Find the value of: $(5^2)^3$
Simplify: $(4x)^2$
Simplify: $(\frac{5}{3})^2$
Find the value of: $25^0$
Simplify: $6^{-2}$
Simplify: $(\frac{4}{9})^{-2}$
Find the value of: $(-1)^{22}$
Find the value of: $(-3)^4$
Solve for $x$: $4^{x+1} = 64$
Simplify: $3^4 \times 3^6$ Explanation: When multiplying terms with the same base, you use the Product Rule and add the exponents. $4 + 6 = 10$, so the result is $3^{10}$.
Simplify: $\frac{7^{10}}{7^4}$ Explanation: When dividing terms with the same base, you use the Quotient Rule and subtract the exponent in the denominator from the exponent in the numerator. $10 – 4 = 6$, giving you $7^6$.
Find the value of: $(5^2)^3$ Explanation: This is the Power of a Power Rule. You multiply the inner exponent by the outer exponent ($2 \times 3 = 6$). $5^6$ equals $15,625$.
Simplify: $(4x)^2$ Explanation: Use the Power of a Product Rule. The exponent outside the parentheses must be applied to every factor inside: $4^2 \times x^2 = 16x^2$.
Simplify: $(\frac{5}{3})^2$ Explanation: This follows the Power of a Quotient Rule. Square both the numerator and the denominator separately: $\frac{5^2}{3^2} = \frac{25}{9}$.
Find the value of: $25^0$ Explanation: The Zero Exponent Rule states that any non-zero number raised to the power of zero is always $1$.
Simplify: $6^{-2}$ Explanation: The Negative Exponent Rule tells us to take the reciprocal of the base to make the exponent positive: $\frac{1}{6^2} = \frac{1}{36}$.
Simplify: $(\frac{4}{9})^{-2}$ Explanation: For a fraction with a negative exponent, flip the fraction (the reciprocal) and change the exponent to positive: $(\frac{9}{4})^2 = \frac{81}{16}$.
Find the value of: $(-1)^{22}$ Explanation: When a negative number is raised to an even power, the result is always positive. Since $22$ is even, the result is $1$.
Find the value of: $(-3)^4$ Explanation: Similar to problem 9, the exponent ($4$) is even. $(-3) \times (-3) \times (-3) \times (-3) = 81$.
Solve for $x$: $4^{x+1} = 64$ Explanation: First, write both sides with the same base. Since $64 = 4^3$, the equation becomes $4^{x+1} = 4^3$. Now you can set the exponents equal to each other: $x + 1 = 3$, which means $x = 2$.