Solve 10 - 1-102-10 - 3-104-105-106

Since, x^a· x^b = x^a+b & x^a/x^b = x^a b So, 10^ 1× 10^2 × 10^ 3× 10^4 ×10^5 ×10^6 = 10^{ 1+2 3+4+5+6} #160; #160; #160; #160; ...

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Standard IX

Mathematics

Laws of Exponents for Real Numbers

Solve 10 - ...

Question

Solve $10^{- 1} \times 10^{2} \times 10^{- 3} \times 10^{4} \times 10^{5} \times 10^{6}$

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Solution

Since, $x^{a} \cdot x^{b} = x^{a + b} & \frac{x^{a}}{x^{b}} = x^{a - b}$
So, $10^{- 1} \times 10^{2} \times 10^{- 3} \times 10^{4} \times 10^{5} \times 10^{6} = 10^{{- 1 + 2 - 3 + 4 + 5 + 6}}$
$= 10^{13}$

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Similar questions

Q. Simplify:

10^{- 1} \times 10^{2} \times 10^{- 3} \times 10^{4} \times 10^{- 5} \times 10^{6}

Write the numeral whose expanded form is given below:
(i) $6 \times 10^{4} + 3 \times 10^{3} + 0 \times 10^{2} + 7 \times 10^{1} + 8 \times 10^{0}$
(ii) $9 \times 10^{6} + 7 \times 10^{5} + 0 \times 10^{4} + 3 \times 10^{3} + 4 \times 10^{2} + 6 \times 10^{1} + 2 \times 10^{0}$
(iii) $8 \times 10^{5} + 6 \times 10^{4} + 4 \times 10^{3} + 2 \times 10^{2} + 9 \times 10^{1} + 6 \times 10^{0}$

Q. Write the number :

4 \times 10^{6} + 8 \times 10^{5} + 6 \times 10^{4} + 4 \times 10^{3} + 4 \times 10^{2} + 6 \times 10 + 9 \times 10^{0}

Q. Solve:

\frac{7}{5} (1 + \frac{1}{10^{2}} + \frac{1.3}{1.2} . \frac{1}{10^{4}} + \frac{1.3.5}{1.2.3} . \frac{1}{10^{6}} + \dots \dots \infty) =

Find the number from each of the following expanded forms:

(a) 8 × 10⁴ + 6 × 10³ + 0 × 10² + 4 × 10¹ + 5 × 10⁰

(b) 4 × 10⁵+ 5 × 10³+ 3 × 10²+ 2 × 10⁰

(d) 9 × 10⁵ + 2 × 10² + 3 × 10¹

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Solve 10−1×102×10−3×104×105×106

Since, xa⋅xb=xa+b&xaxb=xa−bSo, 10−1×102×10−3×104×105×106=10{−1+2−3+4+5+6} =1013

Solve $10^{- 1} \times 10^{2} \times 10^{- 3} \times 10^{4} \times 10^{5} \times 10^{6}$

Since, $x^{a} \cdot x^{b} = x^{a + b} & \frac{x^{a}}{x^{b}} = x^{a - b}$
So, $10^{- 1} \times 10^{2} \times 10^{- 3} \times 10^{4} \times 10^{5} \times 10^{6} = 10^{{- 1 + 2 - 3 + 4 + 5 + 6}}$
$= 10^{13}$