Question

Match the values of $?$, $\ast$ and $\#$ for the following:
${10}^{?}=10,000,000$
${10}^{\ast }=10$
${10}^{\#}=1$

• A. $0$
• B. $7$
• C. $1$

Answer 1

$\bullet {10}^{?}=10,000,000$

First we need to find out to get $10,000,000$, how many times we need to multiply $10$.

As $10,000,000$ has $7$ zeros, $10$ needs to be multiplied $7$ times.

Hence,
$10\times 10\times 10\times 10\times 10\times 10\times 10=10,000,000$
$\Rightarrow {10}^7=10,000,000$
$\Rightarrow {10}^7={10}^{?}$
$\Rightarrow ?=7$

$\underset{–}{\text{Another approach:}}$ In $10,000,000$, we find $7$ zeros. So, if we convert $10,000,000$ in exponent form, the exponent should be $7$.

$\therefore 10,000,000={10}^7\Rightarrow ?=7$
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$\bullet \bullet {10}^{\ast }=10$

We know $10$ is $10$ to the $1^{\text{st}}$ power, i.e., $10={10}^1$.

$\therefore {10}^{\ast }=10={10}^1\Rightarrow \ast =1$

$\underset{–}{\text{Another approach:}}$ In $10$, we find $1$ zero. So, if we convert $10$ in exponent form, the exponent should be $1$.

$\therefore 10={10}^1\Rightarrow \ast =1$
----------------------
$\bullet \bullet \bullet {10}^{\#}=1$

We know $1$ is always a non-zero number with $0^{\text{th}}$ power.

$\therefore {10}^{\#}=1={10}^0\Rightarrow \#=0$