For a - bm - c - bn - ac - bm - n - if ac - bm - n is in scientific notation- then-

Detailed step by step solution: nbsp; (a nbsp;× b^m ) nbsp;× nbsp; (c nbsp;× nbsp; b^n ) = (ac nbsp;× nbsp; b^m + n ) P nbsp; × 10^Q nbsp; ...

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Byju's Answer

Standard VII

Physics

Speed (Average Speed)

For a × bm × ...

Question

For $(a \times b^{m}) \times (c \times b^{n}) = (a c \times b^{m + n}), if (a c \times b^{m + n})$ is in scientific notation, then:

1 \leq a c < 10, b = 10

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1 \leq a c \leq 10, b = 1

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1 \leq a c \leq 10, b = 10

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0 \leq a c \leq 10, b = 10

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Solution

The correct option is A $1 \leq a c < 10, b = 10$
Detailed step-by-step solution:
$(a \times b^{m}) \times (c \times b^{n}) = (a c \times b^{m + n})$

$P \times 10^{Q}$ is said to be in scientific notation if $1 \leq P < 10$ , and the exponent $Q$ is a positive or negative integer.

Given $(a c \times b^{m + n})$ is in scientific notation.

$\Rightarrow 1 \leq a c < 10, b = 10$

➡Option C is correct.

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\frac{{(\frac{a}{b})}^{m}}{{(\frac{a}{b})}^{n}} = {(\frac{a}{b})}^{m - n}

Question 20

For non-zero numbers $a$ and $b$ , ${(\frac{a}{b})}^{m} \div {(\frac{a}{b})}^{n},$ where $m > n,$ is equal to:
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(b) ${(\frac{a}{b})}^{m + n}$
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(d) ${({(\frac{a}{b})}^{m})}^{n}$

Q. Show that:

\frac{{(a + \frac{1}{b})}^{m} \times {(a - \frac{1}{b})}^{n}}{{(b + \frac{1}{a})}^{m} \times {(b - \frac{1}{a})}^{n}} = {(\frac{a}{b})}^{m + n}

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For (a×bm)×(c×bn)=(ac×bm+n),if (ac×bm+n) is in scientific notation, then:

The correct option is A 1≤ac<10,b=10Detailed step-by-step solution: (a×bm)×(c×bn)=(ac×bm+n) P×10Q is said to be in scientific notation if 1≤P<10, and the exponent Q is a positive or negative integer. Given (ac×bm+n) is in scientific notation. ⇒1≤ac<10,b=10 ➡Option C is correct.

For $(a \times b^{m}) \times (c \times b^{n}) = (a c \times b^{m + n}), if (a c \times b^{m + n})$ is in scientific notation, then: