Question

another word for exponent is
write the following examples in exponential form:
3×3×3×3 =
5×5 =
8×8×8×8×8×8 =
write the following in expanded form:
4³ =
9⁵ =
12⁸ =
write the following in standard form:
10³ =
3⁵ =
7⁴ =

Explanation:

Step1: Exponential Form (First Column)

For \(3 \times 3 \times 3 \times 3\), the base is 3 and it is multiplied 4 times, so it is \(3^4\).
For \(5 \times 5\), the base is 5 and multiplied 2 times, so it is \(5^2\).
For \(8 \times 8 \times 8 \times 8 \times 8 \times 8\), the base is 8 and multiplied 6 times, so it is \(8^6\).

Step2: Expanded Form (Second Column)

For \(4^3\), the base is 4 and exponent is 3, so it expands to \(4 \times 4 \times 4\).
For \(9^5\), the base is 9 and exponent is 5, so it expands to \(9 \times 9 \times 9 \times 9 \times 9\).
For \(12^8\), the base is 12 and exponent is 8, so it expands to \(12 \times 12 \times 12 \times 12 \times 12 \times 12 \times 12 \times 12\).

Step3: Standard Form (Third Column)

For \(10^3\), \(10^3 = 10 \times 10 \times 10 = 1000\).
For \(3^5\), \(3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243\).
For \(7^4\), \(7^4 = 7 \times 7 \times 7 \times 7 = 2401\).

Step4: Another Word for Exponent

Another word for exponent is "power" (or "index" in some contexts, but "power" is common here).

Answer:

• Another word for exponent: power
• Exponential Form:

\(3 \times 3 \times 3 \times 3 = \boldsymbol{3^4}\)
\(5 \times 5 = \boldsymbol{5^2}\)
\(8 \times 8 \times 8 \times 8 \times 8 \times 8 = \boldsymbol{8^6}\)

• Expanded Form:

\(4^3 = \boldsymbol{4 \times 4 \times 4}\)
\(9^5 = \boldsymbol{9 \times 9 \times 9 \times 9 \times 9}\)
\(12^8 = \boldsymbol{12 \times 12 \times 12 \times 12 \times 12 \times 12 \times 12 \times 12}\)

• Standard Form:

\(10^3 = \boldsymbol{1000}\)
\(3^5 = \boldsymbol{243}\)
\(7^4 = \boldsymbol{2401}\)