Question

PL ANSWER THIS IF U KNOW THEN ONLY AND NO SPAM ANSWER IF IT IS CORRECT U WILL BE MARK AS BRAINLEST​​

Answer 1

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Answer 2

QUESTION PATTERN:

• INDICES

ANSWER IN IMAGE PLEASE FOLLOW IT :

WE USED CERTAIN FORMULAS WHILE SOLVING THE ABOVE:

• ${x}^{a} \: \div {x}^{b} \: = \: {x}^{a + b}$
• ${x}^{a} \div {x}^{b} \: = \: {x}^{a - b}$
• $( {x}^{a} )^{b} = {x}^{ab}$
• ${a}^{0} = 1$
• ${a}^{ - b} = 1 \div {a}^{b}$

What are indices?

• The indices are also known as powers or exponents. It shows the number of times a given number has to be multiplied. It is represented in the form:

• (indices) in Maths is the power or exponent which is raised to a number or a variable. For example, in number 24, 4 is the index of 2. The plural form of index is indices. In algebra, we come across constants and variables. The constant is a value which cannot be changed. Whereas a variable quantity can be assigned any number or we can say its value can be changed. In algebra, we deal with indices in terms of numbers.

RULES OF INDICES:

• Rule 1: If a constant or variable has index as ‘0’, then the result will be equal to one, regardless of any base value.

• Rule 2: If the index is a negative value, then it can be shown as the reciprocal of the positive index raised to the same variable.

• Rule 3: To multiply two variables with the same base, we need to add its powers and raise them to that base.

• Rule 4: To divide two variables with the same base, we need to subtract the power of denominator from the power of numerator and raise it to that base.

• Rule 5: When a variable with some index is again raised with different index, then both the indices are multiplied together raised to the power of the same base.

• Rule 6: When two variables with different bases, but same indices are multiplied together, we have to multiply its base and raise the same index to multiplied variables.

• Rule 7: When two variables with different bases, but same indices are divided, we are required to divide the bases and raise the same index to it.

• Rule 8: An index in the form of a fraction can be represented as the radical form.