Question

(625)^0.16×(625)^0.09

Answer 1

Answer:

$625^{0.25}$

Step-by-step explanation:

Step 1: Everyday activities include the use of numbers. Numerols are a common name for them. Without numbers, we are unable to count items, dates, hours, money, etc. These numerals are sometimes used for labelling and occasionally for measuring. Numbers are able to execute mathematical operations on them due to their inherent characteristics. Both quantitative and verbal expressions of these quantities are available. As an illustration, the number 2 is written as 2, the number 25 as 25, etc. To learn further, students might practise writing the numbers from 1 to 100 in words.

Step 2: A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of expressing numbers that uses digits or symbols to represent them.

Step 3: $625^{0.16} \times 625^{0.09}$

Apply exponent rule: $\quad a^b \times a^c=a^{b+c}$

$\begin{aligned}& 625^{0.16} \times 625^{0.09}=625^{0.16+0.09} \\& =625^{0.16+0.09}\end{aligned}$

Add the numbers: 0.16+0.09=0.25

=$625^{0.25}$

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Answer 2

$625^{0.16} .625^{0.09} = 4.$

• A number's exponent indicates how many times the number has been multiplied by itself. Exponents are necessary since, without them, it is highly challenging to express the product when a number is repeated several times by itself.
• Exponent-related problems are solved using the rules of exponents or the properties of exponents. These characteristics are regarded as major exponents rules that must be adhered to when solving exponents. How many times we must multiply the reciprocal of the base is indicated by a negative exponent.
• A fractional exponent is one where the exponent of a number is a fraction. Parts of fractional exponents include square roots, cube roots, and nth roots.

Here, according to the given information, we are given that,

$625^{0.16} .625^{0.09}$.

Now, we know that,

$a^{b} .a^{c} = a^{b+c} .$

Applying this, we get,

$625^{0.16} .625^{0.09}\\=625^{0.16+0.09} \\=625^{0.25} \\\\=625^{\frac{25}{100} } \\=625^{\frac{1}{4} } \\\\=5.$

Hence, $625^{0.16} .625^{0.09} = 4.$

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