Question

write the integers as powers.

1. \\(81 = 3 \times \underline{\quad}\\)

\\(= 3 \times \underline{\quad} \times \underline{\quad}\\)
\\(= 3 \times \underline{\quad} \times \underline{\quad} \times \underline{\quad}\\)
\\(= \underline{\quad}\\)

1. 125 as a power of 5 \\(\underline{\quad}\\)
2. 1296 as a power of 6 \\(\underline{\quad}\\)
3. 243 as a power of 3 \\(\underline{\quad}\\)
4. 10 000 as a power of 10 \\(\underline{\quad}\\)
5. 1024 as a power of 4 \\(\underline{\quad}\\)
6. 128 as a power of 2 \\(\underline{\quad}\\)

Explanation:

Factorize 81 step-by-step

Using the Prime Factorization and Exponents knowledge points:
We break down 81 into factors of 3:

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Express 125 and 1296 as powers

Using the Exponents knowledge point:

• For 125 as a power of 5:

$$ 125 = 5 \times 5 \times 5 = 5^3 $$

• For 1296 as a power of 6:

$$ 1296 = 6 \times 6 \times 6 \times 6 = 6^4 $$

Express 243 and 10 000 as powers

Using the Exponents knowledge point:

• For 243 as a power of 3:

$$ 243 = 3 \times 3 \times 3 \times 3 \times 3 = 3^5 $$

• For 10 000 as a power of 10:

$$ 10\,000 = 10 \times 10 \times 10 \times 10 = 10^4 $$

Express 1024 and 128 as powers

Using the Exponents knowledge point:

• For 1024 as a power of 4:

$$ 1024 = 4 \times 4 \times 4 \times 4 \times 4 = 4^5 $$

• For 128 as a power of 2:

$$ 128 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^7 $$

Answer:

Question 10

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Questions 11–16

No.	Problem	Answer
12	1296 as a power of 6	\(6^4\)
13	243 as a power of 3	\(3^5\)
14	10 000 as a power of 10	\(10^4\)
15	1024 as a power of 4	\(4^5\)
16	128 as a power of 2	\(2^7\)