Question

5. Express in exponential form.
(a) 3125 x 32
(b) 240 x 135​

Answer 1

Answer:

3125 × 32

= 1,00,000

${10}^{5} \\ = 100000$

240 × 135

= 32,400

${6}^{4} \times {5}^{2}$

Step-by-step explanation:

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Answer 2

Answer:

$(a) \: \: \: {5}^{5} \times {2}^{5} = {10}^{5} \\ (b) \: \: \: {2}^{4} \times {5}^{2} \times {3}^{4} = {6}^{4} \times {5}^{2} = 324 \times {10}^{2}$

Step-by-step explanation:

$(a) \: we \: know \: that \\ {x}^{a} \times {y}^{a} = {(xy)}^{a} \\ therefore \\ 3125 = {5}^{5} and \: 32 = {2}^{5} \\ so \: {5}^{5} \times {2}^{5} = \: {(2 \times 5)}^{5} = {10}^{5} \\ \\ (b) \: 240 = {2}^{4} \times 3 \times 5 \\ 135 = 5 \times {3}^{3} \\ therefore \\ 240 \times 135 = {2}^{4} \times 3 \times 5 \times 5 \times {3}^{3} = {2}^{4} \times {3}^{4} \times {5}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {(2 \times 3)}^{4} \times {5}^{2} = {6}^{4} \times {5}^{2} = 32400$