Identify Bases and Exponents: Identify the bases and the exponents in the expression. In the expression (8^{-8})(8^{3}), the base is 8 for both terms, with exponents -8 and 3 respectively. Base: 8 Exponents: -8, 3Apply Law of Exponents: Apply the law of exponents for multiplying with the same base. When multiplying terms with the same base, we add the exponents. (8^{-8})(8^{3}) = 8^{-8 + 3}Perform Exponent Addition: Perform the addition of the exponents. -8 + 3 = -5 So, (8^{-8})(8^{3}) = 8^{-5}Evaluate with Simplified Exponent: Evaluate the expression with the simplified exponent. 8^{-5} means 1 divided by 8 raised to the 5th power. 8^{-5} = 1 / (8^5)Calculate Exponentiation: Calculate 8 raised to the 5th power. 8^5 = 8 × 8 × 8 × 8 × 8 = 32768Divide to Find Value: Divide 1 by 32768 to find the value of 8^{-5}. 8^{-5} = 1 / 32768Write Final Answer: Write the final answer. (8^{-8})(8^{3}) = 8^{-5} = 1 / 32768

Grade 8

Powers with negative bases

Full solution

(8^{-8})(8^{3})=\Box

Identify Bases and Exponents: Identify the bases and the exponents in the expression. $\newline$ In the expression $(8^{-8})(8^{3})$ , the base is $8$ for both terms, with exponents $-8$ and $3$ respectively. $\newline$ Base: $8$ $\newline$ Exponents: $-8$ , $3$
Apply Law of Exponents: Apply the law of exponents for multiplying with the same base. $\newline$ When multiplying terms with the same base, we add the exponents. $\newline$ $(8^{-8})(8^{3}) = 8^{-8 + 3}$
Perform Exponent Addition: Perform the addition of the exponents. $\newline$ $-8 + 3 = -5$ $\newline$ So, $(8^{-8})(8^{3}) = 8^{-5}$
Evaluate with Simplified Exponent: Evaluate the expression with the simplified exponent. $\newline$ $8^{-5}$ means $1$ divided by $8$ raised to the $5$ th power. $\newline$ $8^{-5} = \frac{1}{8^5}$
Calculate Exponentiation: Calculate $8$ raised to the $5$ th power. $\newline$ $8^5 = 8 \times 8 \times 8 \times 8 \times 8 = 32768$
Divide to Find Value: Divide $1$ by $32768$ to find the value of $8^{-5}$ . $\newline$ $8^{-5} = 1 / 32768$
Write Final Answer: Write the final answer. $\newline$ $(8^{-8})(8^{3}) = 8^{-5} = 1 / 32768$