Question

Write the base and index of the following numbers:

(1) (–1)²⁰
(2) 7⁵
(3) a⁵
(4) (–2)⁴
(5) 10¹⁰⁰
(6) ${\left(\frac{3}{11}\right)}^9$
(7) ${\left(-\frac{7}{13}\right)}^{10}$
(8) a⁶
(9) (xy)³
(10) ${\left(\frac{a}{b}\right)}^2$

Answer 1

(1) (–1)²⁰ = (–1) × (–1) × (–1) × … 20 times
Here (–1) is the base and 20 is the index.

(2) 7⁵ = 7 × 7 ×7 × 7 ×7
Here 7 is the base and 5 is the index.

(3) a⁵ = a × a × a × a × a
Here a is the base and 5 is the index.

(4) (–2)⁴ = (–2) × (–2) ×(–2) ×(–2)
Here (–2) is the base and 4 is the index.

(5) 10¹⁰⁰ = 10 × 10 ×10 × … 100 times
Here 10 is the base and 100 is the index.

(6) ${\left(\frac{3}{11}\right)}^9=\frac{3}{11}\times \frac{3}{11}\times \frac{3}{11}\times \frac{3}{11}\times \frac{3}{11}\times \frac{3}{11}\times \frac{3}{11}\times \frac{3}{11}\times \frac{3}{11}$
Here $\frac{3}{11}$ is the base and 9 is the index.

(7) ${\left(-\frac{7}{13}\right)}^{10}=\left(-\frac{7}{13}\right)\times \left(-\frac{7}{13}\right)\times \left(-\frac{7}{13}\right)\times \left(-\frac{7}{13}\right)\times \left(-\frac{7}{13}\right)\times \left(-\frac{7}{13}\right)\times \left(-\frac{7}{13}\right)\times \left(-\frac{7}{13}\right)\times \left(-\frac{7}{13}\right)\times \left(-\frac{7}{13}\right)$
Here $\left(-\frac{7}{13}\right)$ is the base and 10 is the index.

(8) a⁶ = a × a × a × a × a × a
Here a is the base and 6 is the index.

(9) (xy)³ = (xy) × (xy) ×(xy)
Here (xy) is the base and 3 is the index.

(10) ${\left(\frac{a}{b}\right)}^2=\frac{a}{b}\times \frac{a}{b}$
Here $\frac{a}{b}$ is the base and 2 is the index.