Exponents

Answer

Step 1: Count how many times 2 is multiplied by itself. Step 2: It is multiplied 5 times. Step 3: So the exponential form is 2^5. Answer: 2 × 2 × 2 × 2 × 2 = 2^5 = 32.

Answer

x^n means x raised to the power n. It means x is multiplied by itself n times. Example: 3^4 = 3 × 3 × 3 × 3 = 81. Here, 3 is the base and 4 is the exponent.

Answer

Step 1: The bases are the same, so add the exponents. Step 2: 3^3 × 3^5 = 3^(3+5) Step 3: 3^8 = 6561 Answer: 6561.

Answer

Use the Product Law when the bases are the same and powers are being multiplied. Formula: a^m × a^n = a^(m+n) Example: 5^2 × 5^3 = 5^(2+3) = 5^5 = 3125. Key idea: same base, so add the exponents.

Answer

Step 1: The bases are the same, so subtract the exponents. Step 2: 2^12 ÷ 2^7 = 2^(12-7) Step 3: 2^5 = 32 Answer: 32.

Answer

Step 1: Since the exponent in the denominator is larger, use the fraction form. Step 2: 2^6 ÷ 2^13 = 1 / 2^(13-6) Step 3: 1 / 2^7 = 1/128 Answer: 1/128.

Answer

Use the Quotient Law when dividing powers with the same base. Formula 1: a^m / a^n = a^(m-n), if m > n Formula 2: a^m / a^n = 1 / a^(n-m), if n > m Example 1: 7^5 / 7^2 = 7^3 = 343 Example 2: 7^2 / 7^…

Answer

Step 1: When a power is raised to another power, multiply the exponents. Step 2: (3^5)^2 = 3^(5×2) Step 3: 3^10 = 59049 Answer: 59049.